NIMCET 2022 — Mathematics PYQ

Solution

Let the given vectors be:

For these vectors to be coplanar, their scalar triple product must be zero:

This can be expressed as the following determinant:

Expanding the determinant along the first row:

Calculating the $2\times 2$ determinants:

Simplifying the equation:

Conclusion

Since $c=\sqrt{ab}$, $c$ is the Geometric Mean of $a$ and $b$.

Correct Option: (B) Geometric mean of $a$ and $b$